What is the integral from 2 to 4 of pi(25-x^2) ?

The integral from 2 to 4 of pi(25-x^2) is pi 94/3

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integral from 2 to 4 of pi(25-x^2)

\int_{2}^{4} π (25 - x^{2}) d x

π \frac{94}{3}

Decimal

98.43656 \dots

Solution steps

\int_{2}^{4} π (25 - x^{2}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \int_{2}^{4} 25 - x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= π (\int_{2}^{4} 25 d x - \int_{2}^{4} x^{2} d x)

\int_{2}^{4} 25 d x = 50

\int_{2}^{4} x^{2} d x = \frac{56}{3}

= π (50 - \frac{56}{3})

Join

50 - \frac{56}{3} : \frac{94}{3}

= π \frac{94}{3}

What is the integral from 2 to 4 of pi(25-x^2) ?
The integral from 2 to 4 of pi(25-x^2) is pi 94/3